x(a+b(c-d))=1

Solution for x(a+b(c-d))=1 equation:

Simplifying
x(a + b(c + -1d)) = 1
x(a + (c * b + -1d * b)) = 1
x(a + (bc + -1bd)) = 1
(a * x + bc * x + -1bd * x) = 1
(ax + bcx + -1bdx) = 1

Solving
ax + bcx + -1bdx = 1

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-1bcx' to each side of the equation.
ax + bcx + -1bcx + -1bdx = 1 + -1bcx

Combine like terms: bcx + -1bcx = 0
ax + 0 + -1bdx = 1 + -1bcx
ax + -1bdx = 1 + -1bcx

Add 'bdx' to each side of the equation.
ax + -1bdx + bdx = 1 + -1bcx + bdx

Combine like terms: -1bdx + bdx = 0
ax + 0 = 1 + -1bcx + bdx
ax = 1 + -1bcx + bdx

Divide each side by 'x'.
a = x-1 + -1bc + bd

Simplifying
a = x-1 + -1bc + bd

Reorder the terms:
a = -1bc + bd + x-1